Mass and Momentum

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Mass Conversion - Mass cannot be created or destroyed. The mass of a closed system can be redistributed at will subject to the constraint that the total mass within the system is constant.

The Linear Momentum of a particle of mass m moving with velocity v is defined to be p = mv = mx' .

Newton's Laws

In an inertial frame every body continues in a state of rest or uniform motion unless acted on by a force.

In an intertial frame the force acting on a body is equal to its rate of change of momentum.

Action and reaction are equal and opposite forces.

An Impulse is a change in momentum (short time, large magnitude).

The Kinetic Energy of a particle of mass m moving with speed v is defined to be K = 1/2 mv^2.

Conservation of Linear Momentum and Collisions

The Rate of Change of Total Linear Momentum is d/dt (p1 + p2) = F12 + F21 and total linear momentum is constant throughout the collision. This gives us the conservation of linear momentum, written as m1u1 + m2u2 = p1 + p2 = m1v1 + m2v2.

Coefficient of Restitution - In a collision between two point particles with inital velocities u1 and u1 and respective final velocities v1 and v2, the relative velocity of particle 1 with respect to particle 2 after impact is related to the same relative velocity before impact by the formula (v1 - v2) = -e (u1 - u2) provided the collision causes "no significant deformation to either body". In the formula the number e is between 0 and 1 and is called the coefficient of restitution for the two bodies. A perfectly elastic collision occurs when e=1 and a perfectly inelastic collision corresponds to the case e=0 (the bodies are fused together).